Rockfish Historical Harvest Estimates

Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases calculated from the sum of the user group releases. The proportion of total rockfish harvested by user group, \(pH_{ayu}\), was assumed to be the mean of \(pH_{(pelagic)ayu}\), \(pH_{(yelloweye)ayu}\) and \(pH_{(nonpel-nonYE)ayu}\) weighted by the relative harvest \(H_{(comp)ayu}\) such that

\[\begin{equation} R_{ayu}~=~ \frac{\sum ({H_{(comp)ayu} * pH_{(comp)ayu})}}{\sum {H_{(comp)ayu}}} \end{equation}\]

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{ayuc})~=~\beta1_{(pH)ayuc} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc}))) + \beta34_{(pH)ayuc}} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
   
3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

• Model: LB_fit_5pH

• Model Run: HR_fitLBR_2bias_hierbeta2_5pH_thru2023_4e+05_7kn_2025-01-08 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.8403

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

• Model development notes:
  • NA

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

Figure 8.- Residuals from logbook harvests

SWHS residuals

Figure 9.- Residuals from SWHS harvests.

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 11.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 13.- Annual proportion of all rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta3_pH 19 2.631666 beta1_pH 17 2.103145 tau_beta0_pH 7 1.867046 beta2_pH 21 1.809276 mu_bc_H 2 1.713553 sd_bc_H 1 1.535581 beta3_pelagic 2 1.515610 beta0_pelagic 3 1.499198 beta0_pH 29 1.447168 tau_beta0_pelagic 1 1.395047

parameter n badRhat_avg beta1_pelagic 4 1.344679 beta2_yellow 2 1.310512 mu_beta0_pH 2 1.270173 beta_H 3 1.257955 beta0_yellow 5 1.245483 beta3_yellow 4 1.232630 beta1_yellow 6 1.207536 beta2_pelagic 4 1.200508 tau_beta0_yellow 1 1.198855 beta2_black 1 1.177858

Table 2. Summary of unconverged parameters by area

	afognak	CI	CSEO	eastside	EWYKT	NG	northeast	NSEI	NSEO	PWSI	PWSO	SOKO2SAP	SSEI	SSEO	WKMA
beta_H	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0
beta0_pelagic	0	0	1	0	0	0	1	0	0	0	1	0	0	0	0
beta0_pH	1	0	1	1	1	1	0	1	1	1	1	1	1	1	0
beta0_yellow	0	0	0	0	1	1	0	1	0	0	1	0	0	1	0
beta1_pelagic	0	0	1	0	0	0	1	1	0	0	1	0	0	0	0
beta1_pH	1	0	1	1	1	1	0	1	0	1	1	0	1	1	0
beta1_yellow	0	0	1	0	1	1	0	1	0	0	1	0	0	1	0
beta2_black	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0
beta2_pelagic	0	0	1	0	1	0	1	1	0	0	0	0	0	0	0
beta2_pH	0	1	1	0	1	1	1	1	1	1	1	1	1	1	0
beta2_yellow	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0
beta3_pelagic	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0
beta3_pH	0	1	1	0	1	0	0	1	1	1	0	0	1	1	1
beta3_yellow	0	0	0	0	1	0	0	1	0	0	0	0	1	1	0
mu_bc_H	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0
mu_beta0_pH	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0
sd_bc_H	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
tau_beta0_pelagic	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
tau_beta0_pH	0	1	0	0	0	1	0	0	0	1	0	0	0	0	0
tau_beta0_yellow	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.133	0.081	-0.276	-0.138	0.040
mu_bc_H[2]	-0.102	0.043	-0.176	-0.106	-0.005
mu_bc_H[3]	-0.425	0.070	-0.558	-0.429	-0.282
mu_bc_H[4]	-0.983	0.189	-1.355	-0.984	-0.615
mu_bc_H[5]	0.748	0.858	-0.277	0.593	2.888
mu_bc_H[6]	-2.235	0.321	-2.836	-2.249	-1.594
mu_bc_H[7]	-0.451	0.111	-0.666	-0.447	-0.236
mu_bc_H[8]	0.279	0.384	-0.336	0.235	1.137
mu_bc_H[9]	-0.363	0.157	-0.682	-0.355	-0.069
mu_bc_H[10]	-0.120	0.071	-0.253	-0.121	0.026
mu_bc_H[11]	-0.108	0.039	-0.183	-0.110	-0.026
mu_bc_H[12]	-0.246	0.104	-0.481	-0.243	-0.046
mu_bc_H[13]	-0.126	0.076	-0.272	-0.126	0.028
mu_bc_H[14]	-0.297	0.097	-0.492	-0.294	-0.117
mu_bc_H[15]	-0.298	0.078	-0.425	-0.308	-0.133
mu_bc_H[16]	-0.189	0.398	-0.853	-0.219	0.687
mu_bc_R[1]	1.476	0.179	1.124	1.477	1.823
mu_bc_R[2]	1.502	0.079	1.338	1.505	1.645
mu_bc_R[3]	1.387	0.146	1.092	1.388	1.670
mu_bc_R[4]	0.984	0.219	0.513	0.993	1.392
mu_bc_R[5]	1.229	0.447	0.346	1.227	2.095
mu_bc_R[6]	-1.560	0.437	-2.411	-1.549	-0.733
mu_bc_R[7]	0.480	0.219	0.018	0.494	0.876
mu_bc_R[8]	0.524	0.198	0.144	0.522	0.915
mu_bc_R[9]	0.452	0.190	0.035	0.469	0.781
mu_bc_R[10]	1.384	0.168	1.061	1.379	1.721
mu_bc_R[11]	1.193	0.057	1.080	1.192	1.303
mu_bc_R[12]	1.030	0.152	0.696	1.036	1.307
mu_bc_R[13]	1.068	0.091	0.883	1.067	1.241
mu_bc_R[14]	1.044	0.133	0.765	1.048	1.289
mu_bc_R[15]	0.831	0.103	0.648	0.826	1.039
mu_bc_R[16]	1.183	0.103	0.976	1.188	1.375
tau_pH[1]	3.122	0.333	2.503	3.112	3.802
tau_pH[2]	1.034	0.409	0.417	1.199	1.592
tau_pH[3]	2.842	0.431	2.077	2.812	3.765
tau_pH[4]	8.308	3.811	3.594	7.529	17.426
tau_pH[5]	3.920	2.034	0.964	3.698	8.420
beta0_pH[1,1]	0.638	0.231	0.155	0.652	1.037
beta0_pH[2,1]	1.253	0.231	0.780	1.255	1.721
beta0_pH[3,1]	1.325	0.312	0.670	1.317	1.979
beta0_pH[4,1]	1.485	0.342	0.807	1.499	2.122
beta0_pH[5,1]	-1.231	0.380	-2.029	-1.218	-0.540
beta0_pH[6,1]	-0.901	0.607	-2.301	-0.820	0.128
beta0_pH[7,1]	-0.017	0.514	-1.102	0.015	0.762
beta0_pH[8,1]	-1.038	0.480	-2.333	-0.924	-0.396
beta0_pH[9,1]	-0.996	0.470	-1.858	-0.950	-0.166
beta0_pH[10,1]	0.504	0.224	0.034	0.509	0.909
beta0_pH[11,1]	0.008	0.735	-1.012	-0.237	1.431
beta0_pH[12,1]	0.588	0.211	0.173	0.590	1.006
beta0_pH[13,1]	-0.507	0.294	-1.082	-0.498	0.050
beta0_pH[14,1]	-0.987	0.338	-1.637	-0.988	-0.328
beta0_pH[15,1]	-0.876	0.490	-1.900	-0.820	-0.074
beta0_pH[16,1]	-1.312	0.938	-2.632	-1.527	0.866
beta0_pH[1,2]	2.599	0.376	1.781	2.629	3.242
beta0_pH[2,2]	2.681	0.500	1.078	2.775	3.302
beta0_pH[3,2]	2.566	0.489	1.567	2.580	3.425
beta0_pH[4,2]	2.655	0.300	1.924	2.681	3.185
beta0_pH[5,2]	3.638	1.566	1.555	3.411	7.059
beta0_pH[6,2]	2.514	0.986	-0.828	2.770	3.518
beta0_pH[7,2]	1.883	0.367	1.114	1.915	2.496
beta0_pH[8,2]	2.631	0.512	1.179	2.729	3.317
beta0_pH[9,2]	2.903	0.856	0.828	3.087	4.027
beta0_pH[10,2]	3.277	0.754	1.371	3.472	4.283
beta0_pH[11,2]	-2.720	0.050	-2.750	-2.738	-2.553
beta0_pH[12,2]	-2.721	0.051	-2.750	-2.738	-2.572
beta0_pH[13,2]	-2.720	0.053	-2.750	-2.738	-2.563
beta0_pH[14,2]	-2.725	0.043	-2.750	-2.739	-2.600
beta0_pH[15,2]	-2.719	0.063	-2.750	-2.739	-2.560
beta0_pH[16,2]	-2.716	0.070	-2.750	-2.738	-2.520
beta0_pH[1,3]	1.180	0.443	-0.072	1.262	1.691
beta0_pH[2,3]	1.574	0.561	0.222	1.574	2.381
beta0_pH[3,3]	1.658	0.385	0.892	1.681	2.360
beta0_pH[4,3]	1.823	0.719	0.528	1.684	3.046
beta0_pH[5,3]	0.648	1.138	-0.717	0.440	3.824
beta0_pH[6,3]	0.003	0.774	-2.174	0.194	1.036
beta0_pH[7,3]	0.496	0.421	-0.638	0.589	1.020
beta0_pH[8,3]	0.308	0.172	-0.033	0.313	0.630
beta0_pH[9,3]	0.182	0.326	-0.479	0.211	0.714
beta0_pH[10,3]	0.436	0.371	-0.422	0.462	1.071
beta0_pH[11,4]	1.460	0.872	-0.775	1.447	2.782
beta0_pH[12,4]	-0.870	1.322	-2.559	-1.251	1.963
beta0_pH[13,4]	0.373	1.623	-2.610	1.015	2.321
beta0_pH[14,4]	1.320	1.180	-1.104	1.417	3.201
beta0_pH[15,4]	0.941	1.776	-2.713	1.156	4.750
beta0_pH[16,4]	1.605	0.652	-0.764	1.729	2.357
beta0_pH[11,5]	-0.847	0.280	-1.337	-0.854	-0.254
beta0_pH[12,5]	-1.676	0.738	-2.681	-1.830	-0.203
beta0_pH[13,5]	-0.601	0.444	-1.534	-0.546	0.083
beta0_pH[14,5]	-1.058	0.312	-1.554	-1.093	-0.169
beta0_pH[15,5]	-0.987	0.381	-1.579	-1.047	-0.012
beta0_pH[16,5]	-0.831	0.267	-1.390	-0.833	-0.257
beta1_pH[1,1]	2.935	0.472	2.118	2.899	3.930
beta1_pH[2,1]	2.282	0.362	1.625	2.265	3.070
beta1_pH[3,1]	2.268	0.593	1.271	2.192	3.766
beta1_pH[4,1]	3.085	0.741	1.979	2.975	4.690
beta1_pH[5,1]	2.564	0.420	1.783	2.546	3.427
beta1_pH[6,1]	3.943	1.064	2.031	3.907	6.214
beta1_pH[7,1]	1.082	0.622	0.204	0.984	2.571
beta1_pH[8,1]	4.403	1.040	2.821	4.250	6.857
beta1_pH[9,1]	2.528	0.520	1.597	2.480	3.526
beta1_pH[10,1]	1.938	0.312	1.399	1.920	2.586
beta1_pH[11,1]	3.530	0.778	1.966	3.755	4.652
beta1_pH[12,1]	2.479	0.252	1.987	2.473	2.995
beta1_pH[13,1]	3.481	0.400	2.752	3.458	4.304
beta1_pH[14,1]	4.292	0.420	3.491	4.283	5.128
beta1_pH[15,1]	4.333	0.648	3.269	4.279	5.777
beta1_pH[16,1]	4.771	0.948	2.470	4.879	6.248
beta1_pH[1,2]	1.692	1.488	0.094	1.287	5.954
beta1_pH[2,2]	1.684	1.777	0.050	1.041	6.932
beta1_pH[3,2]	1.521	1.007	0.149	1.355	4.432
beta1_pH[4,2]	2.370	1.877	0.087	1.936	6.676
beta1_pH[5,2]	3.186	1.954	0.216	2.964	7.508
beta1_pH[6,2]	1.937	1.313	0.151	1.698	5.402
beta1_pH[7,2]	1.948	1.829	0.047	1.344	6.512
beta1_pH[8,2]	1.631	1.607	0.041	1.088	5.921
beta1_pH[9,2]	1.674	1.356	0.088	1.355	5.368
beta1_pH[10,2]	1.905	1.630	0.102	1.414	6.314
beta1_pH[11,2]	4.151	0.861	2.582	4.563	5.160
beta1_pH[12,2]	4.835	0.427	4.028	4.822	5.736
beta1_pH[13,2]	5.218	0.324	4.505	5.232	5.844
beta1_pH[14,2]	4.683	0.314	4.004	4.689	5.306
beta1_pH[15,2]	5.274	0.330	4.573	5.287	5.894
beta1_pH[16,2]	4.942	0.811	3.350	5.314	5.903
beta1_pH[1,3]	2.213	0.637	1.405	2.114	4.036
beta1_pH[2,3]	1.506	1.350	0.128	1.111	5.731
beta1_pH[3,3]	1.106	0.475	0.288	1.071	2.188
beta1_pH[4,3]	1.528	1.029	0.107	1.432	4.409
beta1_pH[5,3]	4.101	1.725	1.315	3.880	8.208
beta1_pH[6,3]	2.748	1.908	0.120	2.418	7.216
beta1_pH[7,3]	1.513	1.603	0.070	0.857	6.061
beta1_pH[8,3]	2.736	0.333	2.068	2.734	3.393
beta1_pH[9,3]	1.883	0.401	1.203	1.854	2.695
beta1_pH[10,3]	2.992	0.476	2.147	2.961	4.041
beta1_pH[11,4]	1.588	1.025	0.100	1.402	3.967
beta1_pH[12,4]	3.921	1.309	1.178	4.269	5.702
beta1_pH[13,4]	3.302	1.706	0.791	3.063	6.252
beta1_pH[14,4]	2.294	1.680	0.115	1.959	6.528
beta1_pH[15,4]	2.671	2.360	0.191	1.748	8.481
beta1_pH[16,4]	1.708	1.520	0.303	1.214	6.811
beta1_pH[11,5]	3.648	1.587	1.486	3.329	7.505
beta1_pH[12,5]	4.571	1.757	1.331	4.415	8.330
beta1_pH[13,5]	4.171	2.241	0.746	3.584	9.528
beta1_pH[14,5]	2.965	1.790	0.341	2.569	7.616
beta1_pH[15,5]	3.225	2.489	0.168	2.701	8.692
beta1_pH[16,5]	3.619	1.865	0.722	3.313	7.980
beta2_pH[1,1]	0.611	0.614	0.242	0.476	2.020
beta2_pH[2,1]	1.308	1.384	0.238	0.741	5.606
beta2_pH[3,1]	1.278	1.446	0.159	0.688	5.595
beta2_pH[4,1]	0.434	0.462	0.138	0.324	1.438
beta2_pH[5,1]	3.455	1.699	1.051	3.135	7.602
beta2_pH[6,1]	0.267	0.467	0.095	0.184	0.956
beta2_pH[7,1]	2.705	2.713	-3.003	2.427	8.419
beta2_pH[8,1]	0.229	0.098	0.101	0.210	0.456
beta2_pH[9,1]	0.779	0.816	0.222	0.530	3.306
beta2_pH[10,1]	1.145	1.123	0.301	0.764	4.622
beta2_pH[11,1]	1.225	1.122	0.451	0.831	4.756
beta2_pH[12,1]	3.210	1.651	1.088	2.827	7.395
beta2_pH[13,1]	0.889	0.545	0.369	0.746	2.314
beta2_pH[14,1]	0.984	0.427	0.542	0.896	2.055
beta2_pH[15,1]	0.601	0.238	0.294	0.554	1.179
beta2_pH[16,1]	0.543	0.569	0.143	0.410	1.858
beta2_pH[1,2]	-0.255	3.229	-6.880	0.246	5.565
beta2_pH[2,2]	-1.690	2.928	-7.688	-1.641	4.555
beta2_pH[3,2]	-2.409	2.390	-7.333	-2.151	2.587
beta2_pH[4,2]	-2.597	2.475	-7.690	-2.476	2.907
beta2_pH[5,2]	0.427	3.021	-6.352	0.702	5.915
beta2_pH[6,2]	-1.638	2.808	-7.197	-1.534	4.473
beta2_pH[7,2]	-2.468	2.608	-7.754	-2.297	3.067
beta2_pH[8,2]	-1.570	3.027	-7.507	-1.629	4.587
beta2_pH[9,2]	-1.221	2.967	-6.777	-1.350	5.056
beta2_pH[10,2]	-1.149	3.162	-7.396	-1.029	5.172
beta2_pH[11,2]	-2.513	3.924	-8.887	-3.575	4.794
beta2_pH[12,2]	-2.083	1.477	-6.205	-1.631	-0.546
beta2_pH[13,2]	-3.753	1.749	-7.912	-3.401	-1.288
beta2_pH[14,2]	-3.549	1.827	-8.351	-3.111	-1.241
beta2_pH[15,2]	-4.675	1.901	-8.780	-4.491	-1.583
beta2_pH[16,2]	-2.764	4.247	-9.091	-4.152	5.425
beta2_pH[1,3]	2.764	1.922	0.232	2.544	6.837
beta2_pH[2,3]	0.955	2.896	-5.666	1.014	5.702
beta2_pH[3,3]	-0.678	2.851	-6.400	0.090	5.746
beta2_pH[4,3]	1.326	2.500	-4.781	1.475	6.712
beta2_pH[5,3]	2.300	2.038	-0.167	2.000	6.924
beta2_pH[6,3]	2.026	2.582	-3.970	1.965	7.224
beta2_pH[7,3]	-0.284	3.094	-6.385	-0.080	5.843
beta2_pH[8,3]	4.944	1.917	1.662	4.815	9.067
beta2_pH[9,3]	3.345	1.625	0.860	3.149	7.065
beta2_pH[10,3]	1.645	1.398	0.410	1.062	5.375
beta2_pH[11,4]	-1.556	2.382	-6.616	-1.332	3.857
beta2_pH[12,4]	-2.206	1.821	-6.569	-1.245	-0.599
beta2_pH[13,4]	0.278	1.911	-3.906	0.436	4.744
beta2_pH[14,4]	-1.021	2.411	-5.774	-1.176	2.902
beta2_pH[15,4]	-1.930	2.607	-7.187	-1.629	1.119
beta2_pH[16,4]	2.268	1.974	-0.957	2.110	6.580
beta2_pH[11,5]	-2.175	1.459	-5.903	-1.780	-0.462
beta2_pH[12,5]	-2.505	1.512	-6.260	-2.546	-0.493
beta2_pH[13,5]	-1.148	1.930	-5.736	-0.300	1.147
beta2_pH[14,5]	-2.797	1.760	-7.168	-2.278	-0.302
beta2_pH[15,5]	-1.829	4.294	-8.211	-3.205	5.029
beta2_pH[16,5]	-1.689	1.448	-5.750	-1.373	-0.106
beta3_pH[1,1]	36.153	1.114	34.096	36.101	38.434
beta3_pH[2,1]	33.023	1.269	30.903	32.907	36.154
beta3_pH[3,1]	34.087	1.406	31.880	33.898	37.612
beta3_pH[4,1]	35.390	1.913	32.239	35.138	39.570
beta3_pH[5,1]	27.269	0.523	26.409	27.218	28.138
beta3_pH[6,1]	37.940	3.256	31.159	38.166	43.398
beta3_pH[7,1]	28.488	6.894	19.905	25.172	43.023
beta3_pH[8,1]	39.209	2.085	34.878	39.230	43.180
beta3_pH[9,1]	29.702	1.713	26.697	29.596	33.186
beta3_pH[10,1]	33.436	1.267	31.068	33.408	35.933
beta3_pH[11,1]	31.032	0.862	29.548	30.925	32.822
beta3_pH[12,1]	30.512	0.467	29.569	30.524	31.320
beta3_pH[13,1]	33.174	0.708	31.863	33.149	34.648
beta3_pH[14,1]	31.934	0.516	30.957	31.934	32.979
beta3_pH[15,1]	32.335	0.836	30.707	32.295	34.048
beta3_pH[16,1]	31.508	2.122	29.357	30.963	37.791
beta3_pH[1,2]	32.662	7.965	19.787	31.709	43.448
beta3_pH[2,2]	29.275	6.315	19.529	28.586	42.161
beta3_pH[3,2]	36.458	7.188	20.622	40.364	43.460
beta3_pH[4,2]	26.723	5.999	19.433	25.026	42.190
beta3_pH[5,2]	30.075	6.443	19.715	29.283	42.736
beta3_pH[6,2]	32.028	5.157	20.772	33.460	40.811
beta3_pH[7,2]	27.230	5.832	19.298	26.445	40.544
beta3_pH[8,2]	28.120	5.985	19.433	27.031	41.935
beta3_pH[9,2]	31.825	8.026	19.831	29.691	43.869
beta3_pH[10,2]	29.476	6.446	19.739	28.368	42.430
beta3_pH[11,2]	37.199	8.507	21.849	43.027	43.581
beta3_pH[12,2]	42.077	0.740	40.428	42.118	43.296
beta3_pH[13,2]	43.373	0.326	42.613	43.389	43.913
beta3_pH[14,2]	42.759	0.446	41.749	42.838	43.497
beta3_pH[15,2]	43.238	0.281	42.530	43.254	43.710
beta3_pH[16,2]	37.464	8.506	20.067	43.223	43.676
beta3_pH[1,3]	39.742	1.259	36.015	39.953	41.328
beta3_pH[2,3]	30.345	5.051	20.241	31.261	40.862
beta3_pH[3,3]	35.227	6.684	21.219	33.623	43.486
beta3_pH[4,3]	27.538	5.405	19.442	27.257	42.925
beta3_pH[5,3]	30.148	5.639	19.850	30.552	39.792
beta3_pH[6,3]	31.135	5.221	20.761	31.113	42.806
beta3_pH[7,3]	27.519	6.148	19.432	26.523	41.762
beta3_pH[8,3]	41.504	0.242	41.041	41.505	41.939
beta3_pH[9,3]	33.850	0.575	32.854	33.834	34.996
beta3_pH[10,3]	35.506	0.821	33.598	35.646	36.782
beta3_pH[11,4]	37.014	6.795	20.408	39.805	44.407
beta3_pH[12,4]	41.903	0.813	39.566	42.064	42.864
beta3_pH[13,4]	36.638	4.678	29.819	35.784	43.141
beta3_pH[14,4]	33.498	7.635	20.015	32.965	43.795
beta3_pH[15,4]	35.354	6.858	20.760	36.144	44.147
beta3_pH[16,4]	35.441	2.701	32.165	34.712	43.891
beta3_pH[11,5]	40.489	1.371	38.104	40.396	43.001
beta3_pH[12,5]	37.858	2.419	34.357	37.751	42.350
beta3_pH[13,5]	36.515	4.700	26.945	37.228	41.634
beta3_pH[14,5]	38.547	4.080	23.433	39.630	41.709
beta3_pH[15,5]	36.516	7.622	20.330	40.717	42.739
beta3_pH[16,5]	37.597	2.594	31.182	38.069	41.153
beta0_pelagic[1]	1.420	0.517	0.442	1.434	2.249
beta0_pelagic[2]	1.308	0.258	0.610	1.362	1.654
beta0_pelagic[3]	0.166	0.293	-0.516	0.219	0.607
beta0_pelagic[4]	0.087	0.424	-0.936	0.176	0.739
beta0_pelagic[5]	1.218	0.285	0.537	1.262	1.645
beta0_pelagic[6]	1.405	0.271	0.759	1.451	1.782
beta0_pelagic[7]	1.358	0.317	0.255	1.433	1.702
beta0_pelagic[8]	1.702	0.167	1.361	1.708	2.008
beta0_pelagic[9]	1.326	0.456	0.186	1.390	2.126
beta0_pelagic[10]	1.955	0.455	1.078	1.982	2.653
beta0_pelagic[11]	0.318	0.306	-0.342	0.367	0.837
beta0_pelagic[12]	1.631	0.148	1.332	1.632	1.909
beta0_pelagic[13]	0.464	0.140	0.201	0.460	0.740
beta0_pelagic[14]	0.130	0.249	-0.432	0.154	0.532
beta0_pelagic[15]	-0.315	0.135	-0.593	-0.311	-0.046
beta0_pelagic[16]	0.272	0.184	-0.121	0.285	0.584
beta1_pelagic[1]	0.898	0.609	0.048	0.839	2.289
beta1_pelagic[2]	0.301	0.265	0.012	0.233	0.995
beta1_pelagic[3]	0.966	0.389	0.423	0.890	2.040
beta1_pelagic[4]	1.117	0.437	0.430	1.031	2.167
beta1_pelagic[5]	0.489	0.431	0.018	0.403	1.446
beta1_pelagic[6]	0.572	0.657	0.018	0.392	2.623
beta1_pelagic[7]	0.531	0.676	0.016	0.336	2.636
beta1_pelagic[8]	0.881	0.665	0.085	0.755	2.532
beta1_pelagic[9]	1.649	0.510	0.794	1.577	2.896
beta1_pelagic[10]	0.998	0.836	0.031	0.770	2.979
beta1_pelagic[11]	2.609	0.544	1.708	2.510	3.850
beta1_pelagic[12]	2.257	0.314	1.666	2.251	2.901
beta1_pelagic[13]	2.019	0.346	1.398	1.983	2.737
beta1_pelagic[14]	3.013	0.509	2.092	2.985	4.091
beta1_pelagic[15]	2.313	0.251	1.787	2.319	2.807
beta1_pelagic[16]	3.257	0.435	2.505	3.216	4.228
beta2_pelagic[1]	2.036	2.236	-2.920	1.823	6.835
beta2_pelagic[2]	1.446	2.254	-3.592	1.221	6.057
beta2_pelagic[3]	1.471	1.554	0.091	0.819	5.599
beta2_pelagic[4]	2.137	1.731	0.261	1.591	6.494
beta2_pelagic[5]	-1.460	2.776	-6.545	-1.553	5.153
beta2_pelagic[6]	0.783	3.005	-5.404	0.875	6.713
beta2_pelagic[7]	-0.855	2.677	-5.683	-0.947	5.102
beta2_pelagic[8]	-1.871	1.792	-6.249	-1.583	0.394
beta2_pelagic[9]	1.743	1.731	0.133	1.066	6.371
beta2_pelagic[10]	0.835	2.080	-3.602	0.158	5.624
beta2_pelagic[11]	0.569	0.558	0.159	0.366	2.158
beta2_pelagic[12]	1.066	0.545	0.416	0.954	2.246
beta2_pelagic[13]	1.042	0.900	0.331	0.731	3.817
beta2_pelagic[14]	0.392	0.179	0.172	0.343	0.878
beta2_pelagic[15]	1.954	1.073	0.854	1.635	5.208
beta2_pelagic[16]	0.624	0.307	0.239	0.558	1.380
beta3_pelagic[1]	24.664	4.118	19.912	23.085	36.115
beta3_pelagic[2]	29.074	5.251	20.104	29.135	38.606
beta3_pelagic[3]	29.456	2.810	23.762	29.777	35.075
beta3_pelagic[4]	25.093	1.902	21.448	25.217	28.852
beta3_pelagic[5]	30.103	4.464	21.289	29.642	38.626
beta3_pelagic[6]	29.548	5.378	20.258	29.433	39.537
beta3_pelagic[7]	28.660	4.522	20.374	28.914	38.116
beta3_pelagic[8]	27.783	3.389	21.518	27.246	35.751
beta3_pelagic[9]	27.238	2.794	23.221	26.422	34.335
beta3_pelagic[10]	27.643	5.025	19.522	27.393	37.926
beta3_pelagic[11]	40.397	2.009	34.423	41.226	41.979
beta3_pelagic[12]	41.775	0.252	41.102	41.854	41.994
beta3_pelagic[13]	41.208	0.643	39.547	41.339	41.963
beta3_pelagic[14]	40.705	1.295	37.052	41.100	41.957
beta3_pelagic[15]	41.824	0.178	41.346	41.879	41.995
beta3_pelagic[16]	41.500	0.525	40.019	41.669	41.987
mu_beta0_pelagic[1]	0.680	0.734	-0.865	0.719	1.911
mu_beta0_pelagic[2]	1.486	0.275	0.902	1.501	1.999
mu_beta0_pelagic[3]	0.406	0.369	-0.322	0.414	1.097
tau_beta0_pelagic[1]	2.425	3.603	0.068	1.314	12.139
tau_beta0_pelagic[2]	17.562	35.905	0.615	6.422	131.524
tau_beta0_pelagic[3]	2.210	1.502	0.325	1.873	5.844
beta0_yellow[1]	-0.592	0.186	-1.005	-0.582	-0.285
beta0_yellow[2]	0.443	0.206	-0.041	0.463	0.763
beta0_yellow[3]	-0.318	0.169	-0.689	-0.308	-0.006
beta0_yellow[4]	0.598	0.381	-0.349	0.679	1.150
beta0_yellow[5]	-1.159	0.427	-2.012	-1.159	-0.306
beta0_yellow[6]	0.182	0.214	-0.238	0.182	0.604
beta0_yellow[7]	0.424	0.725	-1.258	0.648	1.301
beta0_yellow[8]	0.785	0.418	-0.384	0.901	1.246
beta0_yellow[9]	-0.078	0.255	-0.574	-0.077	0.405
beta0_yellow[10]	0.237	0.150	-0.052	0.239	0.525
beta0_yellow[11]	-0.183	0.202	-0.619	-0.170	0.181
beta0_yellow[12]	-3.174	0.610	-4.364	-3.187	-1.879
beta0_yellow[13]	-3.575	0.539	-4.636	-3.585	-2.514
beta0_yellow[14]	-0.396	0.324	-1.323	-0.333	0.063
beta0_yellow[15]	-2.451	0.423	-3.358	-2.424	-1.540
beta0_yellow[16]	-0.796	0.739	-2.844	-0.508	-0.061
beta1_yellow[1]	0.550	0.588	0.019	0.393	2.027
beta1_yellow[2]	1.269	0.465	0.723	1.179	2.685
beta1_yellow[3]	0.723	0.256	0.316	0.699	1.321
beta1_yellow[4]	2.007	0.878	0.854	1.790	4.135
beta1_yellow[5]	3.221	1.202	1.358	3.081	6.248
beta1_yellow[6]	2.348	0.352	1.657	2.347	3.035
beta1_yellow[7]	1.561	1.379	0.060	1.215	5.640
beta1_yellow[8]	1.941	1.630	0.090	1.453	5.965
beta1_yellow[9]	1.476	0.362	0.807	1.466	2.153
beta1_yellow[10]	2.723	0.503	1.800	2.697	3.801
beta1_yellow[11]	1.597	1.110	0.253	1.272	4.811
beta1_yellow[12]	2.279	0.995	0.967	2.145	5.260
beta1_yellow[13]	2.900	0.732	1.726	2.823	4.897
beta1_yellow[14]	1.291	0.947	0.120	1.013	3.679
beta1_yellow[15]	1.862	0.614	1.003	1.768	3.522
beta1_yellow[16]	0.986	0.820	0.035	0.760	2.910
beta2_yellow[1]	-1.664	2.568	-6.761	-1.491	4.171
beta2_yellow[2]	-1.788	1.748	-6.474	-1.125	-0.106
beta2_yellow[3]	-2.348	1.813	-6.825	-1.928	-0.140
beta2_yellow[4]	-0.874	1.327	-4.885	-0.287	-0.072
beta2_yellow[5]	-2.940	1.870	-7.336	-2.620	-0.457
beta2_yellow[6]	3.249	1.637	1.017	2.995	7.115
beta2_yellow[7]	0.410	3.195	-6.110	0.548	6.181
beta2_yellow[8]	-1.401	2.494	-6.111	-1.344	4.551
beta2_yellow[9]	3.565	1.808	0.530	3.329	7.642
beta2_yellow[10]	-3.479	1.809	-7.642	-3.194	-0.824
beta2_yellow[11]	-1.850	1.671	-5.920	-1.342	-0.115
beta2_yellow[12]	-2.734	1.906	-7.101	-2.504	-0.073
beta2_yellow[13]	-2.687	1.471	-6.370	-2.443	-0.112
beta2_yellow[14]	-1.635	1.709	-5.834	-1.136	-0.036
beta2_yellow[15]	-2.494	1.791	-6.803	-2.128	-0.079
beta2_yellow[16]	-0.310	3.177	-6.206	-0.598	6.470
beta3_yellow[1]	29.077	4.771	20.295	29.539	37.677
beta3_yellow[2]	29.185	1.839	25.222	29.044	33.149
beta3_yellow[3]	32.532	2.035	28.249	32.547	36.633
beta3_yellow[4]	28.772	2.896	22.794	28.458	34.761
beta3_yellow[5]	32.995	1.318	30.035	33.102	34.954
beta3_yellow[6]	39.518	0.486	38.560	39.500	40.605
beta3_yellow[7]	27.816	3.664	20.796	27.731	36.337
beta3_yellow[8]	28.171	3.506	21.062	28.291	35.267
beta3_yellow[9]	37.395	1.086	35.972	37.450	38.647
beta3_yellow[10]	29.293	0.482	28.099	29.361	30.012
beta3_yellow[11]	31.535	1.818	29.136	31.313	35.701
beta3_yellow[12]	41.828	3.394	31.178	43.092	44.180
beta3_yellow[13]	43.983	2.592	32.432	44.627	44.985
beta3_yellow[14]	32.380	2.238	29.139	32.274	37.267
beta3_yellow[15]	43.853	2.314	34.921	44.550	44.986
beta3_yellow[16]	31.412	2.481	29.039	30.540	38.198
mu_beta0_yellow[1]	0.015	0.449	-0.895	0.015	0.944
mu_beta0_yellow[2]	0.059	0.420	-0.815	0.065	0.896
mu_beta0_yellow[3]	-1.499	0.800	-3.131	-1.499	0.197
tau_beta0_yellow[1]	3.558	5.021	0.195	2.245	14.339
tau_beta0_yellow[2]	2.370	3.299	0.252	1.591	8.957
tau_beta0_yellow[3]	0.377	0.322	0.037	0.297	1.180
beta0_black[1]	-0.091	0.152	-0.392	-0.087	0.198
beta0_black[2]	1.668	0.339	0.678	1.747	2.042
beta0_black[3]	1.153	0.335	0.268	1.219	1.518
beta0_black[4]	1.795	0.425	0.582	1.896	2.282
beta0_black[5]	1.354	1.177	-0.961	1.344	3.438
beta0_black[6]	1.359	1.337	-1.045	1.348	3.241
beta0_black[7]	1.397	1.423	-0.939	1.353	3.462
beta0_black[8]	1.137	0.300	0.430	1.173	1.621
beta0_black[9]	1.663	0.512	0.719	1.644	2.568
beta0_black[10]	1.355	0.143	1.071	1.362	1.632
beta0_black[11]	3.330	0.271	2.709	3.366	3.691
beta0_black[12]	4.398	0.182	4.053	4.398	4.752
beta0_black[13]	-0.081	0.220	-0.528	-0.074	0.338
beta0_black[14]	1.779	0.625	0.206	1.939	2.598
beta0_black[15]	1.026	0.355	0.065	1.102	1.512
beta0_black[16]	3.271	0.950	0.701	3.560	4.343
beta2_black[1]	3.163	1.736	0.821	2.797	7.367
beta2_black[2]	-1.622	2.352	-6.603	-1.385	4.124
beta2_black[3]	-0.123	3.129	-6.369	0.012	6.147
beta2_black[4]	-1.987	1.937	-6.868	-1.407	-0.052
beta2_black[5]	0.012	3.185	-6.154	-0.076	6.284
beta2_black[6]	0.031	3.164	-6.351	-0.050	6.365
beta2_black[7]	-0.012	3.128	-6.104	-0.066	6.170
beta2_black[8]	-3.135	2.158	-7.580	-2.931	0.093
beta2_black[9]	-1.456	2.488	-6.513	-1.082	4.296
beta2_black[10]	-1.018	2.786	-6.233	-1.106	5.250
beta2_black[11]	-1.740	1.720	-5.865	-1.436	0.751
beta2_black[12]	-2.973	1.610	-6.989	-2.642	-0.786
beta2_black[13]	-1.965	1.338	-5.403	-1.549	-0.432
beta2_black[14]	-0.904	1.342	-5.034	-0.321	-0.083
beta2_black[15]	-1.768	2.100	-6.754	-1.273	2.092
beta2_black[16]	1.687	1.949	-1.255	1.222	6.424
beta3_black[1]	41.803	0.971	40.245	41.915	43.055
beta3_black[2]	29.908	7.971	19.231	30.587	44.365
beta3_black[3]	27.776	7.334	19.214	27.336	44.437
beta3_black[4]	32.744	3.862	21.873	32.807	40.335
beta3_black[5]	31.928	7.468	19.644	32.112	45.053
beta3_black[6]	31.967	7.235	19.852	31.766	45.137
beta3_black[7]	31.802	7.147	19.839	31.415	44.733
beta3_black[8]	28.425	7.845	20.132	23.257	42.899
beta3_black[9]	34.568	8.317	19.645	35.664	45.158
beta3_black[10]	28.400	9.269	19.346	23.942	45.272
beta3_black[11]	33.558	3.939	29.159	32.295	43.152
beta3_black[12]	32.869	0.591	31.527	32.943	33.806
beta3_black[13]	39.249	0.745	37.603	39.323	40.453
beta3_black[14]	38.137	3.648	30.386	38.447	44.979
beta3_black[15]	35.864	5.025	29.188	35.052	45.306
beta3_black[16]	33.703	4.190	29.140	32.292	43.935
beta4_black[1]	-0.274	0.188	-0.641	-0.279	0.090
beta4_black[2]	0.281	0.176	-0.074	0.281	0.629
beta4_black[3]	-0.997	0.180	-1.349	-0.995	-0.642
beta4_black[4]	0.638	0.219	0.212	0.638	1.062
beta4_black[5]	0.032	3.145	-6.142	0.048	5.898
beta4_black[6]	0.069	3.210	-6.120	0.028	6.552
beta4_black[7]	-0.028	3.216	-6.197	-0.062	6.240
beta4_black[8]	-0.836	0.364	-1.559	-0.836	-0.114
beta4_black[9]	2.138	1.095	0.322	2.025	4.499
beta4_black[10]	0.034	0.180	-0.323	0.036	0.385
beta4_black[11]	-0.718	0.220	-1.158	-0.715	-0.294
beta4_black[12]	0.572	0.333	-0.075	0.564	1.244
beta4_black[13]	-1.286	0.214	-1.718	-1.282	-0.890
beta4_black[14]	-0.040	0.244	-0.522	-0.043	0.440
beta4_black[15]	-0.940	0.217	-1.361	-0.939	-0.526
beta4_black[16]	-0.595	0.236	-1.051	-0.589	-0.141
mu_beta0_black[1]	1.032	0.826	-0.774	1.092	2.442
mu_beta0_black[2]	1.313	0.664	0.108	1.346	2.306
mu_beta0_black[3]	1.951	1.154	-0.758	2.085	3.838
tau_beta0_black[1]	1.283	1.165	0.054	0.987	4.416
tau_beta0_black[2]	19.060	30.295	0.088	5.829	111.743
tau_beta0_black[3]	0.313	0.222	0.022	0.267	0.859
beta0_dsr[11]	-3.098	0.284	-3.636	-3.108	-2.492
beta0_dsr[12]	4.574	0.297	4.001	4.579	5.152
beta0_dsr[13]	-1.702	0.478	-2.832	-1.643	-0.891
beta0_dsr[14]	-4.247	0.383	-4.911	-4.268	-3.475
beta0_dsr[15]	-2.391	0.282	-2.928	-2.379	-1.853
beta0_dsr[16]	-3.112	0.339	-3.804	-3.114	-2.447
beta1_dsr[11]	4.946	0.298	4.342	4.957	5.505
beta1_dsr[12]	4.333	1.769	1.432	4.123	8.327
beta1_dsr[13]	3.690	0.911	2.524	3.460	6.179
beta1_dsr[14]	6.911	0.421	6.075	6.923	7.659
beta1_dsr[15]	3.539	0.286	2.991	3.529	4.080
beta1_dsr[16]	5.904	0.358	5.221	5.902	6.614
beta2_dsr[11]	-6.292	1.479	-9.439	-6.219	-3.679
beta2_dsr[12]	-3.342	1.777	-7.507	-3.058	-0.697
beta2_dsr[13]	-1.551	1.611	-5.693	-0.712	-0.162
beta2_dsr[14]	-3.668	1.297	-6.872	-3.410	-1.830
beta2_dsr[15]	-5.176	1.605	-8.636	-5.025	-2.407
beta2_dsr[16]	-5.524	1.454	-8.671	-5.370	-3.042
beta3_dsr[11]	43.480	0.128	43.245	43.479	43.724
beta3_dsr[12]	33.483	0.966	31.164	33.709	34.768
beta3_dsr[13]	42.270	1.265	39.007	42.792	43.683
beta3_dsr[14]	43.380	0.143	43.142	43.368	43.694
beta3_dsr[15]	43.443	0.167	43.139	43.441	43.768
beta3_dsr[16]	43.450	0.132	43.208	43.442	43.723
beta4_dsr[11]	0.741	0.220	0.304	0.741	1.190
beta4_dsr[12]	0.184	0.701	-1.098	0.160	1.684
beta4_dsr[13]	-0.173	0.219	-0.608	-0.172	0.256
beta4_dsr[14]	0.183	0.275	-0.362	0.181	0.722
beta4_dsr[15]	1.108	0.214	0.679	1.112	1.522
beta4_dsr[16]	0.163	0.241	-0.303	0.159	0.636
beta0_slope[11]	-1.995	0.161	-2.308	-1.996	-1.677
beta0_slope[12]	-4.598	0.230	-4.971	-4.616	-4.125
beta0_slope[13]	-1.605	0.301	-2.372	-1.558	-1.175
beta0_slope[14]	-2.753	0.191	-3.128	-2.753	-2.378
beta0_slope[15]	-1.703	0.170	-2.048	-1.696	-1.383
beta0_slope[16]	-2.824	0.170	-3.154	-2.826	-2.495
beta1_slope[11]	4.396	0.298	3.815	4.400	4.962
beta1_slope[12]	5.059	0.552	3.965	5.060	6.146
beta1_slope[13]	2.792	0.579	1.999	2.673	4.234
beta1_slope[14]	5.967	0.697	4.700	5.942	7.441
beta1_slope[15]	2.000	0.298	1.438	2.001	2.584
beta1_slope[16]	5.323	0.404	4.559	5.319	6.103
beta2_slope[11]	6.088	1.551	3.335	5.997	9.237
beta2_slope[12]	3.761	1.790	1.192	3.531	7.876
beta2_slope[13]	2.012	1.587	0.247	1.666	5.933
beta2_slope[14]	1.320	0.383	0.777	1.260	2.253
beta2_slope[15]	4.245	1.695	1.562	4.032	7.992
beta2_slope[16]	5.324	1.589	2.664	5.127	8.778
beta3_slope[11]	43.486	0.138	43.229	43.484	43.767
beta3_slope[12]	43.355	0.268	42.829	43.344	43.868
beta3_slope[13]	43.068	0.885	40.517	43.287	44.144
beta3_slope[14]	44.304	0.349	43.569	44.314	44.930
beta3_slope[15]	43.627	0.292	43.114	43.617	44.205
beta3_slope[16]	43.471	0.151	43.206	43.462	43.776
beta4_slope[11]	-0.487	0.220	-0.917	-0.486	-0.051
beta4_slope[12]	-2.405	0.772	-4.042	-2.377	-1.038
beta4_slope[13]	0.294	0.218	-0.124	0.291	0.728
beta4_slope[14]	-0.018	0.265	-0.521	-0.014	0.523
beta4_slope[15]	-0.171	0.221	-0.592	-0.171	0.271
beta4_slope[16]	-0.064	0.239	-0.528	-0.064	0.415
sigma_H[1]	0.215	0.056	0.117	0.209	0.341
sigma_H[2]	0.175	0.030	0.126	0.172	0.240
sigma_H[3]	0.190	0.041	0.116	0.187	0.278
sigma_H[4]	0.418	0.077	0.291	0.409	0.586
sigma_H[5]	0.976	0.216	0.582	0.968	1.423
sigma_H[6]	0.401	0.195	0.059	0.391	0.828
sigma_H[7]	0.314	0.067	0.214	0.303	0.475
sigma_H[8]	0.417	0.083	0.279	0.409	0.603
sigma_H[9]	0.549	0.133	0.333	0.534	0.844
sigma_H[10]	0.209	0.043	0.135	0.205	0.301
sigma_H[11]	0.276	0.045	0.201	0.272	0.378
sigma_H[12]	0.448	0.164	0.215	0.433	0.773
sigma_H[13]	0.215	0.038	0.148	0.210	0.297
sigma_H[14]	0.511	0.092	0.353	0.506	0.709
sigma_H[15]	0.253	0.045	0.180	0.248	0.353
sigma_H[16]	0.219	0.042	0.149	0.215	0.313
lambda_H[1]	2.531	3.455	0.125	1.452	11.169
lambda_H[2]	8.402	7.778	0.871	6.131	27.965
lambda_H[3]	6.340	9.822	0.227	3.082	33.084
lambda_H[4]	0.006	0.004	0.001	0.005	0.017
lambda_H[5]	3.164	9.038	0.025	0.661	24.767
lambda_H[6]	7.200	15.114	0.009	0.699	51.491
lambda_H[7]	0.012	0.009	0.002	0.010	0.034
lambda_H[8]	8.515	10.726	0.163	4.821	37.420
lambda_H[9]	0.015	0.010	0.003	0.012	0.039
lambda_H[10]	0.279	0.492	0.028	0.187	0.992
lambda_H[11]	0.239	0.314	0.012	0.133	1.014
lambda_H[12]	4.958	6.397	0.181	2.897	23.695
lambda_H[13]	3.321	3.122	0.232	2.397	11.850
lambda_H[14]	3.458	4.524	0.209	2.042	15.395
lambda_H[15]	0.038	0.195	0.004	0.018	0.153
lambda_H[16]	0.714	1.120	0.040	0.368	3.225
mu_lambda_H[1]	4.358	1.901	1.273	4.190	8.393
mu_lambda_H[2]	3.805	1.950	0.631	3.669	7.914
mu_lambda_H[3]	3.524	1.908	0.707	3.231	7.866
sigma_lambda_H[1]	8.642	4.299	1.946	8.094	18.245
sigma_lambda_H[2]	8.387	4.678	1.021	7.786	18.378
sigma_lambda_H[3]	6.272	3.981	0.982	5.391	15.619
beta_H[1,1]	6.813	1.189	3.985	7.019	8.580
beta_H[2,1]	9.876	0.495	8.782	9.904	10.808
beta_H[3,1]	7.955	0.810	5.949	8.053	9.221
beta_H[4,1]	9.662	7.830	-6.870	9.956	24.397
beta_H[5,1]	-0.008	2.562	-5.332	0.149	4.530
beta_H[6,1]	3.103	4.055	-6.661	4.563	7.841
beta_H[7,1]	0.020	6.099	-13.150	0.460	10.768
beta_H[8,1]	1.207	2.903	-2.263	1.190	3.519
beta_H[9,1]	13.244	5.805	2.147	13.219	24.634
beta_H[10,1]	7.094	1.732	3.648	7.093	10.550
beta_H[11,1]	5.252	3.343	-2.484	5.920	10.031
beta_H[12,1]	2.608	1.041	0.665	2.558	4.915
beta_H[13,1]	9.036	0.946	6.999	9.133	10.499
beta_H[14,1]	2.213	1.045	0.229	2.212	4.207
beta_H[15,1]	-5.397	4.338	-12.712	-5.746	4.020
beta_H[16,1]	3.645	2.789	-0.851	3.255	10.297
beta_H[1,2]	7.906	0.261	7.374	7.911	8.395
beta_H[2,2]	10.027	0.135	9.763	10.026	10.291
beta_H[3,2]	8.941	0.205	8.550	8.939	9.355
beta_H[4,2]	3.497	1.469	0.750	3.478	6.491
beta_H[5,2]	1.957	0.999	0.025	1.971	3.904
beta_H[6,2]	5.756	1.111	3.242	5.940	7.497
beta_H[7,2]	2.794	1.134	0.758	2.726	5.309
beta_H[8,2]	3.035	0.894	1.580	3.116	4.270
beta_H[9,2]	3.577	1.126	1.403	3.546	5.859
beta_H[10,2]	8.188	0.361	7.434	8.190	8.885
beta_H[11,2]	9.717	0.596	8.833	9.605	11.133
beta_H[12,2]	3.941	0.374	3.256	3.925	4.716
beta_H[13,2]	9.116	0.254	8.653	9.107	9.627
beta_H[14,2]	4.025	0.362	3.329	4.013	4.752
beta_H[15,2]	11.199	0.786	9.578	11.261	12.564
beta_H[16,2]	4.489	0.845	2.992	4.453	6.261
beta_H[1,3]	8.500	0.262	8.003	8.493	9.044
beta_H[2,3]	10.079	0.114	9.857	10.080	10.309
beta_H[3,3]	9.619	0.165	9.302	9.613	9.957
beta_H[4,3]	-2.465	0.907	-4.231	-2.439	-0.727
beta_H[5,3]	4.012	0.664	2.704	4.014	5.314
beta_H[6,3]	8.202	1.203	6.544	7.867	10.804
beta_H[7,3]	-2.912	0.693	-4.342	-2.893	-1.566
beta_H[8,3]	5.180	0.421	4.574	5.134	6.028
beta_H[9,3]	-2.819	0.765	-4.331	-2.802	-1.351
beta_H[10,3]	8.746	0.280	8.212	8.747	9.314
beta_H[11,3]	8.552	0.276	7.971	8.568	9.060
beta_H[12,3]	5.244	0.313	4.481	5.280	5.748
beta_H[13,3]	8.824	0.184	8.445	8.830	9.171
beta_H[14,3]	5.681	0.276	5.049	5.703	6.152
beta_H[15,3]	10.349	0.336	9.687	10.343	11.014
beta_H[16,3]	6.065	0.605	4.729	6.116	7.102
beta_H[1,4]	8.225	0.197	7.788	8.242	8.573
beta_H[2,4]	10.137	0.117	9.888	10.146	10.345
beta_H[3,4]	10.095	0.167	9.725	10.110	10.387
beta_H[4,4]	11.756	0.450	10.862	11.761	12.649
beta_H[5,4]	5.790	0.851	4.414	5.687	7.717
beta_H[6,4]	7.141	0.945	5.018	7.431	8.402
beta_H[7,4]	8.300	0.360	7.574	8.304	9.004
beta_H[8,4]	6.689	0.234	6.259	6.691	7.113
beta_H[9,4]	7.415	0.587	6.347	7.379	8.688
beta_H[10,4]	7.737	0.235	7.292	7.735	8.221
beta_H[11,4]	9.289	0.201	8.890	9.288	9.691
beta_H[12,4]	7.127	0.223	6.727	7.117	7.593
beta_H[13,4]	9.012	0.142	8.723	9.013	9.286
beta_H[14,4]	7.675	0.216	7.269	7.671	8.104
beta_H[15,4]	9.391	0.257	8.879	9.393	9.878
beta_H[16,4]	9.301	0.242	8.864	9.290	9.815
beta_H[1,5]	8.994	0.157	8.681	9.002	9.301
beta_H[2,5]	10.785	0.094	10.602	10.785	10.977
beta_H[3,5]	10.908	0.172	10.615	10.894	11.285
beta_H[4,5]	8.399	0.464	7.532	8.386	9.346
beta_H[5,5]	5.322	0.655	3.821	5.403	6.414
beta_H[6,5]	8.835	0.614	7.972	8.693	10.338
beta_H[7,5]	6.756	0.348	6.076	6.754	7.442
beta_H[8,5]	8.211	0.204	7.847	8.201	8.602
beta_H[9,5]	8.248	0.496	7.253	8.246	9.217
beta_H[10,5]	10.119	0.224	9.682	10.120	10.558
beta_H[11,5]	11.553	0.224	11.096	11.554	11.987
beta_H[12,5]	8.469	0.200	8.076	8.470	8.871
beta_H[13,5]	10.014	0.129	9.769	10.013	10.267
beta_H[14,5]	9.213	0.239	8.788	9.198	9.718
beta_H[15,5]	11.086	0.278	10.524	11.087	11.630
beta_H[16,5]	9.944	0.172	9.596	9.947	10.285
beta_H[1,6]	10.257	0.209	9.901	10.234	10.751
beta_H[2,6]	11.520	0.108	11.306	11.522	11.732
beta_H[3,6]	10.816	0.164	10.460	10.827	11.102
beta_H[4,6]	12.866	0.826	11.167	12.902	14.388
beta_H[5,6]	5.863	0.648	4.710	5.822	7.188
beta_H[6,6]	8.744	0.662	6.996	8.880	9.693
beta_H[7,6]	9.868	0.587	8.730	9.856	11.039
beta_H[8,6]	9.535	0.267	9.065	9.551	9.985
beta_H[9,6]	8.511	0.830	6.914	8.496	10.144
beta_H[10,6]	9.512	0.320	8.860	9.538	10.094
beta_H[11,6]	10.814	0.362	10.040	10.833	11.479
beta_H[12,6]	9.375	0.257	8.893	9.362	9.909
beta_H[13,6]	11.073	0.163	10.783	11.063	11.429
beta_H[14,6]	9.884	0.301	9.287	9.895	10.472
beta_H[15,6]	10.886	0.428	10.023	10.893	11.691
beta_H[16,6]	10.527	0.248	9.974	10.541	10.964
beta_H[1,7]	10.861	1.017	8.204	11.033	12.380
beta_H[2,7]	12.229	0.427	11.361	12.233	13.046
beta_H[3,7]	10.568	0.680	9.067	10.636	11.704
beta_H[4,7]	2.509	4.157	-5.316	2.408	10.747
beta_H[5,7]	6.435	2.069	2.904	6.284	11.120
beta_H[6,7]	9.514	2.490	4.683	9.427	15.826
beta_H[7,7]	10.485	2.949	4.610	10.569	16.278
beta_H[8,7]	10.971	0.982	9.440	10.927	12.527
beta_H[9,7]	4.591	4.233	-3.979	4.671	12.938
beta_H[10,7]	9.906	1.481	7.184	9.832	13.075
beta_H[11,7]	10.991	1.745	7.693	10.896	14.880
beta_H[12,7]	10.016	0.927	7.857	10.107	11.592
beta_H[13,7]	11.676	0.762	9.778	11.791	12.840
beta_H[14,7]	10.523	0.952	8.414	10.602	12.244
beta_H[15,7]	11.806	2.230	7.326	11.775	16.293
beta_H[16,7]	12.475	1.353	10.257	12.297	15.517
beta0_H[1]	8.821	15.241	-22.107	9.002	37.319
beta0_H[2]	10.749	6.324	-2.036	10.697	23.991
beta0_H[3]	9.704	10.413	-12.152	9.851	31.227
beta0_H[4]	5.381	182.338	-350.795	4.793	375.096
beta0_H[5]	4.285	30.524	-55.351	4.562	63.343
beta0_H[6]	8.056	50.275	-96.840	7.524	118.424
beta0_H[7]	1.972	140.621	-295.019	3.621	283.255
beta0_H[8]	6.865	24.987	-12.583	6.631	27.806
beta0_H[9]	7.708	125.135	-244.611	5.704	263.532
beta0_H[10]	8.985	34.618	-61.200	8.585	81.030
beta0_H[11]	9.618	48.600	-94.086	8.980	109.285
beta0_H[12]	6.391	11.059	-15.749	6.526	28.009
beta0_H[13]	9.991	11.134	-10.024	9.935	29.966
beta0_H[14]	6.993	11.872	-17.971	7.096	28.673
beta0_H[15]	7.478	103.977	-205.716	8.374	224.364
beta0_H[16]	7.510	29.017	-47.219	7.244	64.218